ceph/src/boost/libs/multiprecision/doc/html/boost_multiprecision/tut/floats/gmp_float.html

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  26 <div class="titlepage"><div><div><h4 class="title">
  27 <a name="boost_multiprecision.tut.floats.gmp_float"></a><a class="link" href="gmp_float.html" title="gmp_float">gmp_float</a>
  28 </h4></div></div></div>
  29 <p>
  30           <code class="computeroutput"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">multiprecision</span><span class="special">/</span><span class="identifier">gmp</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span></code>
  31         </p>
  32 <pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">multiprecision</span><span class="special">{</span>
  33
  34 <span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">unsigned</span> <span class="identifier">Digits10</span><span class="special">&gt;</span>
  35 <span class="keyword">class</span> <span class="identifier">gmp_float</span><span class="special">;</span>
  36
  37 <span class="keyword">typedef</span> <span class="identifier">number</span><span class="special">&lt;</span><span class="identifier">gmp_float</span><span class="special">&lt;</span><span class="number">50</span><span class="special">&gt;</span> <span class="special">&gt;</span>    <span class="identifier">mpf_float_50</span><span class="special">;</span>
  38 <span class="keyword">typedef</span> <span class="identifier">number</span><span class="special">&lt;</span><span class="identifier">gmp_float</span><span class="special">&lt;</span><span class="number">100</span><span class="special">&gt;</span> <span class="special">&gt;</span>   <span class="identifier">mpf_float_100</span><span class="special">;</span>
  39 <span class="keyword">typedef</span> <span class="identifier">number</span><span class="special">&lt;</span><span class="identifier">gmp_float</span><span class="special">&lt;</span><span class="number">500</span><span class="special">&gt;</span> <span class="special">&gt;</span>   <span class="identifier">mpf_float_500</span><span class="special">;</span>
  40 <span class="keyword">typedef</span> <span class="identifier">number</span><span class="special">&lt;</span><span class="identifier">gmp_float</span><span class="special">&lt;</span><span class="number">1000</span><span class="special">&gt;</span> <span class="special">&gt;</span>  <span class="identifier">mpf_float_1000</span><span class="special">;</span>
  41 <span class="keyword">typedef</span> <span class="identifier">number</span><span class="special">&lt;</span><span class="identifier">gmp_float</span><span class="special">&lt;</span><span class="number">0</span><span class="special">&gt;</span> <span class="special">&gt;</span>     <span class="identifier">mpf_float</span><span class="special">;</span>
  42
  43 <span class="special">}}</span> <span class="comment">// namespaces</span>
  44 </pre>
  45 <p>
  46           The <code class="computeroutput"><span class="identifier">gmp_float</span></code> back-end
  47           is used in conjunction with <code class="computeroutput"><span class="identifier">number</span></code>
  48           : it acts as a thin wrapper around the <a href="http://gmplib.org" target="_top">GMP</a>
  49           <code class="computeroutput"><span class="identifier">mpf_t</span></code> to provide an real-number
  50           type that is a drop-in replacement for the native C++ floating-point types,
  51           but with much greater precision.
  52         </p>
  53 <p>
  54           Type <code class="computeroutput"><span class="identifier">gmp_float</span></code> can be used
  55           at fixed precision by specifying a non-zero <code class="computeroutput"><span class="identifier">Digits10</span></code>
  56           template parameter, or at variable precision by setting the template argument
  57           to zero. The typedefs mpf_float_50, mpf_float_100, mpf_float_500, mpf_float_1000
  58           provide arithmetic types at 50, 100, 500 and 1000 decimal digits precision
  59           respectively. The typedef mpf_float provides a variable precision type
  60           whose precision can be controlled via the <code class="computeroutput"><span class="identifier">number</span></code>s
  61           member functions.
  62         </p>
  63 <div class="note"><table border="0" summary="Note">
  64 <tr>
  65 <td rowspan="2" align="center" valign="top" width="25"><img alt="[Note]" src="../../../../../../../doc/src/images/note.png"></td>
  66 <th align="left">Note</th>
  67 </tr>
  68 <tr><td align="left" valign="top"><p>
  69             This type only provides standard library and <code class="computeroutput"><span class="identifier">numeric_limits</span></code>
  70             support when the precision is fixed at compile time.
  71           </p></td></tr>
  72 </table></div>
  73 <p>
  74           As well as the usual conversions from arithmetic and string types, instances
  75           of <code class="computeroutput"><span class="identifier">number</span><span class="special">&lt;</span><span class="identifier">mpf_float</span><span class="special">&lt;</span><span class="identifier">N</span><span class="special">&gt;</span> <span class="special">&gt;</span></code> are copy constructible and assignable
  76           from:
  77         </p>
  78 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
  79 <li class="listitem">
  80               The <a href="http://gmplib.org" target="_top">GMP</a> native types <code class="computeroutput"><span class="identifier">mpf_t</span></code>, <code class="computeroutput"><span class="identifier">mpz_t</span></code>,
  81               <code class="computeroutput"><span class="identifier">mpq_t</span></code>.
  82             </li>
  83 <li class="listitem">
  84               The <code class="computeroutput"><span class="identifier">number</span></code> wrappers
  85               around those types: <code class="computeroutput"><span class="identifier">number</span><span class="special">&lt;</span><span class="identifier">mpf_float</span><span class="special">&lt;</span><span class="identifier">M</span><span class="special">&gt;</span> <span class="special">&gt;</span></code>,
  86               <code class="computeroutput"><span class="identifier">number</span><span class="special">&lt;</span><span class="identifier">gmp_int</span><span class="special">&gt;</span></code>,
  87               <code class="computeroutput"><span class="identifier">number</span><span class="special">&lt;</span><span class="identifier">gmp_rational</span><span class="special">&gt;</span></code>.
  88             </li>
  89 </ul></div>
  90 <p>
  91           It's also possible to access the underlying <code class="computeroutput"><span class="identifier">mpf_t</span></code>
  92           via the <code class="computeroutput"><span class="identifier">data</span><span class="special">()</span></code>
  93           member function of <code class="computeroutput"><span class="identifier">gmp_float</span></code>.
  94         </p>
  95 <p>
  96           Things you should know when using this type:
  97         </p>
  98 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
  99 <li class="listitem">
 100               Default constructed <code class="computeroutput"><span class="identifier">gmp_float</span></code>s
 101               have the value zero (this is the <a href="http://gmplib.org" target="_top">GMP</a>
 102               library's default behavior).
 103             </li>
 104 <li class="listitem">
 105               No changes are made to the <a href="http://gmplib.org" target="_top">GMP</a>
 106               library's global settings, so this type can be safely mixed with existing
 107               <a href="http://gmplib.org" target="_top">GMP</a> code.
 108             </li>
 109 <li class="listitem">
 110               This backend supports rvalue-references and is move-aware, making instantiations
 111               of <code class="computeroutput"><span class="identifier">number</span></code> on this backend
 112               move aware.
 113             </li>
 114 <li class="listitem">
 115               It is not possible to round-trip objects of this type to and from a
 116               string and get back exactly the same value. This appears to be a limitation
 117               of <a href="http://gmplib.org" target="_top">GMP</a>.
 118             </li>
 119 <li class="listitem">
 120               Since the underlying <a href="http://gmplib.org" target="_top">GMP</a> types
 121               have no notion of infinities or NaN's, care should be taken to avoid
 122               numeric overflow or division by zero. That latter will result in a
 123               std::overflow_error being thrown, while generating excessively large
 124               exponents may result in instability of the underlying <a href="http://gmplib.org" target="_top">GMP</a>
 125               library (in testing, converting a number with an excessively large
 126               or small exponent to a string caused <a href="http://gmplib.org" target="_top">GMP</a>
 127               to segfault).
 128             </li>
 129 <li class="listitem">
 130               This type can equally be used with <a href="http://mpir.org/" target="_top">MPIR</a>
 131               as the underlying implementation - indeed that is the recommended option
 132               on Win32.
 133             </li>
 134 <li class="listitem">
 135               Conversion from a string results in a <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">runtime_error</span></code>
 136               being thrown if the string can not be interpreted as a valid floating-point
 137               number.
 138             </li>
 139 <li class="listitem">
 140               Division by zero results in a <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">overflow_error</span></code>
 141               being thrown.
 142             </li>
 143 </ul></div>
 144 <h6>
 145 <a name="boost_multiprecision.tut.floats.gmp_float.h0"></a>
 146           <span class="phrase"><a name="boost_multiprecision.tut.floats.gmp_float.gmp_example"></a></span><a class="link" href="gmp_float.html#boost_multiprecision.tut.floats.gmp_float.gmp_example"> GMP example:</a>
 147         </h6>
 148 <pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">multiprecision</span><span class="special">/</span><span class="identifier">gmp</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
 149 <span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">special_functions</span><span class="special">/</span><span class="identifier">gamma</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
 150 <span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">iostream</span><span class="special">&gt;</span>
 151
 152 <span class="keyword">int</span> <span class="identifier">main</span><span class="special">()</span>
 153 <span class="special">{</span>
 154    <span class="keyword">using</span> <span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">multiprecision</span><span class="special">;</span>
 155
 156    <span class="comment">// Operations at variable precision and limited standard library support:</span>
 157    <span class="identifier">mpf_float</span> <span class="identifier">a</span> <span class="special">=</span> <span class="number">2</span><span class="special">;</span>
 158    <span class="identifier">mpf_float</span><span class="special">::</span><span class="identifier">default_precision</span><span class="special">(</span><span class="number">1000</span><span class="special">);</span>
 159    <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">mpf_float</span><span class="special">::</span><span class="identifier">default_precision</span><span class="special">()</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
 160    <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">sqrt</span><span class="special">(</span><span class="identifier">a</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span> <span class="comment">// print root-2</span>
 161
 162    <span class="comment">// Operations at fixed precision and full standard library support:</span>
 163    <span class="identifier">mpf_float_100</span> <span class="identifier">b</span> <span class="special">=</span> <span class="number">2</span><span class="special">;</span>
 164    <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special">&lt;</span><span class="identifier">mpf_float_100</span><span class="special">&gt;::</span><span class="identifier">digits</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
 165    <span class="comment">// We can use any C++ std lib function:</span>
 166    <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">log</span><span class="special">(</span><span class="identifier">b</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span> <span class="comment">// print log(2)</span>
 167    <span class="comment">// We can also use any function from Boost.Math:</span>
 168    <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">tgamma</span><span class="special">(</span><span class="identifier">b</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
 169    <span class="comment">// These even work when the argument is an expression template:</span>
 170    <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">tgamma</span><span class="special">(</span><span class="identifier">b</span> <span class="special">*</span> <span class="identifier">b</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
 171
 172    <span class="comment">// Access the underlying representation:</span>
 173    <span class="identifier">mpf_t</span> <span class="identifier">f</span><span class="special">;</span>
 174    <span class="identifier">mpf_init</span><span class="special">(</span><span class="identifier">f</span><span class="special">);</span>
 175    <span class="identifier">mpf_set</span><span class="special">(</span><span class="identifier">f</span><span class="special">,</span> <span class="identifier">a</span><span class="special">.</span><span class="identifier">backend</span><span class="special">().</span><span class="identifier">data</span><span class="special">());</span>
 176    <span class="identifier">mpf_clear</span><span class="special">(</span><span class="identifier">f</span><span class="special">);</span>
 177    <span class="keyword">return</span> <span class="number">0</span><span class="special">;</span>
 178 <span class="special">}</span>
 179 </pre>
 180 </div>
 181 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 182 <td align="left"></td>
 183 <td align="right"><div class="copyright-footer">Copyright &#169; 2002-2013 John Maddock and Christopher Kormanyos<p>
 184         Distributed under the Boost Software License, Version 1.0. (See accompanying
 185         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
 186       </p>
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